Competitions

# 9 Round Spiral. Round 3. Step 5.

# ATM

In some country in circulation there are notes of certain denominations. National Bank wants the cash machine to give out any requested amount with a minimum number of banknotes, considering that the amount of banknotes of each denomination is unlimited.

Help the National Bank to solve this problem.

#### Input

First line contains the number of banknotes denominations in circulation **n** (**n** ≤ **100**). Second line contains **n** different positive integers `x`

, _{1}`x`

, ..., _{2}`x`

not greater than _{n}`10`

- the banknotes denominations. Third line contains the sum ^{6}**s** (**s** ≤ `10`

) that you want to give.^{6}

#### Output

Print in the first line the minimal number of summands (or **-1** if such representation does not exist). In the second line print these summands in any order.

Input example #1

5 1 3 7 12 32 40

Output example #1

3 32 7 1